Error-correcting two-dimensional modulation codes

Abstract

Modulation coding, to limit the number of consecutive zeroes in a data stream, is essential in digital magnetic recording/playback systems. Additionally, such systems require error correction coding to ensure that the decoded output matches the recorder input, even if noise is present. Typically these two coding steps have been performed independently, although various methods of combining them into one step have recently appeared. Another recent development is two-dimensional modulation codes, which meet runlength constraints using several parallel recording tracks, significantly increasing channel capacity. This thesis combines these two ideas. Previous techniques (both block and trellis structures) for combining error correction and modulation coding are surveyed, with discussion of their applicability in the two-dimensional case. One approach, based on trellis-coded modulation, is explored in detail, and a class of codes developed which exploit the increased capacity to achieve good error-correcting ability at the same rate as common non-error-correcting one-dimensional codes.